Two people stand around a circular duck pond of radius R. They are placed randomly along the circumference of the duck pond. What is the probability that the distance between them is greater than R?
+128472 They will be R distance apart whenever we have an equilateral triangle with one vertex at the center of the circle and the other two vertexes on the circle.......the sides will = R
And the central angle formed by the two sides of R each will be 60°
So.....the probability that the distance between them will be > R is given by
1 - 60/360 =
1 - 1/6 =
5/6
